SUSTech becomes bigger and bigger. The president wants to make the campus more convenient.

He decided
to set n stations in the campus. The stations are built according **the DSAA
first law**: for i-th station, it is served as the original station for i-th bus line. For each station, it is served as the destination station for only one bus line. For each bus line, the bus in it goes to the destination station directly. Please note that the original and destination station could be the same for some bus lines.

The convenience of the station building plan is measured by **the ****DSAA second law****: **we use (x, y) to denote we can go from
station x and arrive at station y, please note that (1) one passenger could take different bus lines to arrive y from x; (2) (x, y) and (y, x) are different, and (3) (x, x) is allowed. The convenience of the total plan is defined as the total number of all possible (x, y) pairs among the n stations, the larger the better.

In order to improve the convenience, now we can change the destination of some bus lines according **the ****DSAA third law: **we can change at most two destinations of distinct bus lines.

Please find the maximum convenience value we can
get by following the DSAA 1^{st}, 2^{nd} and 3^{rd} laws. All stations are labeled from 1 to n.